Problem: $77$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $63$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 77}$ ${x = 3y-63}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-63}$ for $x$ in the first equation. ${(3y-63)}{+ y = 77}$ Simplify and solve for $y$ $ 3y-63 + y = 77 $ $ 4y-63 = 77 $ $ 4y = 140 $ $ y = \dfrac{140}{4} $ ${y = 35}$ Now that you know ${y = 35}$ , plug it back into ${x = 3y-63}$ to find $x$ ${x = 3}{(35)}{ - 63}$ $x = 105 - 63$ ${x = 42}$ You can also plug ${y = 35}$ into ${x+y = 77}$ and get the same answer for $x$ ${x + }{(35)}{= 77}$ ${x = 42}$ There were $42$ home team fans and $35$ away team fans.